Elements of GeometryHarper & brothers, 1896 - 540 sider |
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Side iii
... called a revision . We have utilized many of the terse and accurate statements and definitions of the Loomis Geometry , and have aimed to maintain the high standard of that work for rigorous demonstrations , but , aside from these ...
... called a revision . We have utilized many of the terse and accurate statements and definitions of the Loomis Geometry , and have aimed to maintain the high standard of that work for rigorous demonstrations , but , aside from these ...
Side iv
... called to the theorems of proportion , the use of corollaries as exercises to supply the need of " inven- tional geometry , " and the Introduction to Modern Geom- etry . We would here express our grateful acknowledgments to all who have ...
... called to the theorems of proportion , the use of corollaries as exercises to supply the need of " inven- tional geometry , " and the Introduction to Modern Geom- etry . We would here express our grateful acknowledgments to all who have ...
Side 1
... called a corollary of the second . A theorem used merely to prepare the way for another theorem is sometimes called a lemma . + plus . minus . SYMBOLS AND ABBREVIATIONS > is greater than . < is less than . x multiplied by . = equals ...
... called a corollary of the second . A theorem used merely to prepare the way for another theorem is sometimes called a lemma . + plus . minus . SYMBOLS AND ABBREVIATIONS > is greater than . < is less than . x multiplied by . = equals ...
Side 3
... called simply solids . Def . - A solid is , then , a limited portion of space . 3. Def . - The boundaries of a solid are surfaces ( that is , the surfaces separate it from the surrounding space ) . A surface is no part of a solid . 4 ...
... called simply solids . Def . - A solid is , then , a limited portion of space . 3. Def . - The boundaries of a solid are surfaces ( that is , the surfaces separate it from the surrounding space ) . A surface is no part of a solid . 4 ...
Side 7
... called the foot of the perpendicular . 17. Def . - An acute angle is an angle less than a right angle ; an obtuse angle , greater . The term oblique angle may be applied to any angle which is not a right angle . PROPOSITION I. THEOREM ...
... called the foot of the perpendicular . 17. Def . - An acute angle is an angle less than a right angle ; an obtuse angle , greater . The term oblique angle may be applied to any angle which is not a right angle . PROPOSITION I. THEOREM ...
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Vanlige uttrykk og setninger
ABCD allel altitude angles are equal apothem base and altitude bisecting bisector centre chord circumference circumscribed coincide cone conical surface construct cylinder Def.-The Defs.-A diagonals diameter diedral angles distance divided draw drawn equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum given line given point given straight line GIVEN TO PROVE given triangle Hence homologous homologous sides hypotenuse intersection lateral area lateral edges lateral faces locus measured by arc middle points number of sides parallel planes parallelogram parallelopiped pass a plane perimeter PLANE GEOMETRY plane MN polyedral angle polyedron prismatic surface Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon square surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Populære avsnitt
Side 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Side 5 - If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.
Side 434 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Side 393 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Side 185 - To construct a square equivalent to the sum of any number of given squares.
Side 390 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Side 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.
Side 476 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.
Side 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.